Magic squares of doubly even order
Magic squares of doubly even order is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
A magic square of doubly even order has a size that is a multiple of four (e.g. 4, 8, 12). This means that the subsquares also have an even size, which plays a role in the construction.
The task: create a magic square of 8 x 8.
- Cf.
- See also
Java
<lang java>public class MagicSquareDoublyEven {
public static void main(String[] args) {
int n = 8;
for (int[] row : magicSquareDoublyEven(n)) {
for (int x : row)
System.out.printf("%2s ", x);
System.out.println();
}
System.out.printf("\nMagic constant: %d ", (n * n + 1) * n / 2);
}
static int[][] magicSquareDoublyEven(final int n) {
if (n < 4 || n % 4 != 0)
throw new IllegalArgumentException("base must be a positive "
+ "multiple of 4");
int bits = 0b1001011001101001;
int size = n * n;
int mult = n / 4;
int[][] result = new int[n][n];
for (int i = 0; i < size; i++) {
int bitsPos = (i % n) / mult + (i / (n * mult) * 4);
int value = (bits & (1 << bitsPos)) != 0 ? i + 1 : size - i;
result[i / n][i % n] = value;
}
return result;
}
}</lang>
1 2 62 61 60 59 7 8 9 10 54 53 52 51 15 16 48 47 19 20 21 22 42 41 40 39 27 28 29 30 34 33 32 31 35 36 37 38 26 25 24 23 43 44 45 46 18 17 49 50 14 13 12 11 55 56 57 58 6 5 4 3 63 64 Magic constant: 260